Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 6 - Systems of Equations and Inequalities - 6-6 Systems of Linear Inequalities - Practice and Problem-Solving Exercises - Page 403: 24


$x$ $\leq$ $1$ $y$ $\lt$ $\dfrac{-3}{2}x+3$

Work Step by Step

The equation is $x$ $\leq$ $1$ because $x=1$ and the left side of the line is shaded. The points $(0,3)$ and $(2,0)$. Find the slope: $m=\dfrac{3-0}{0-2}$ $m={-\dfrac{3}{2}}$ The slope equation is $y=mx+b$ $y=mx+b$ $0=-{\dfrac{3}{3}}(2)+b$ $0=-3+b$ $3=b$ The equation is $y$ $\lt$ $\dfrac{-3}{2}x+3$ because $(0,0)$ is not included in the solution area.
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